$\begingroup$Asking about the "best" way is likely to result in a lot of opinion based answers. Consider revising your question to something like "is there an effective method..." or "what methods have been used..." That way, your question may become a useful reference for future seekers. :-)$\endgroup$
– Chris ThompsonOct 18 '16 at 23:45

3 Answers
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While the "best" method is probably unanswerable since it would be based on very specific requirements and subject to change as soon as a better method were devised, here are some feasible methods to auto-eject 3d printed parts.

Some of these are methods that I've considered for my personal use, others have been mentioned by others and added for helpful reference. Some have been done, others have not (I think), but all of them are feasible.

Scrolling Conveyor-type Bed:

In this concept, parts become dislodged from the print surface as it is deformed around a roller in the process of scrolling to the next position. Scrolling bed designs must make allowances to prevent parts from lifting up the bed material which becomes an issue especially with warp-prone materials. Note: This is the basis of the Automated Build Platform (ABP) originally designed (as far as I can tell) by Charles Pax and later covered in several patents by Makerbot Industries.

Deforming Bed:

In this concept, the bed is mechanically deformed when the part removal temperature has been reached. This deformation dislodges the part which can then be easily swept off of the bed by an arm or similar mechanism. (As far as I know, this concept has not yet been demonstrated.)

Articulated Segmented Bed:

In this concept, the bed is comprised of several strips. Slightly lowering a portion (let's say half) of the strips would separate them from the part, then slightly raising that portion would separate the part from the remaining strips. (As far as I know, this concept has not yet been demonstrated.)

Eject and Replace Bed:

This method ejects the entire bed surface along with the finished parts and then receives a fresh print surface for the next print. This method would likely still require intervention to remove parts from used print surfaces and then return them to the clean stack. (As far as I know, this concept has not yet been demonstrated.)

Plow:

This method mentioned by Fred_dot_u and AllanL uses a specially designed plow arm to sweep parts off the bed between prints. This method has been effectively demonstrated in this video by New Valance Robotics Corporation that was mentioned by AllanL (thanks!).

Issues using print head to eject parts: While this method has been tried, and demonstrated (see below), it has some challenges/drawbacks.

Typical FDM/FFF 3d printers are not designed to apply significant force behind print head movements. While a printer designed specifically for this purpose could be built, using a typical printer in this way is extremely likely to cause the stepper motors to loose steps and result in loss of position accuracy unless parts separate very easily. (however, position could easily be regained by zeroing via limit switches between prints.)

In addition to skipping steps, mechanical issues such as ratcheting/skipping belts or unwanted frame movement could result from even moderately stuck prints.

Examples of pushing or ramming parts off of bed:
While using various parts of the printer to push parts off of the bed may not be an ideal solution, it may be an adequate solution for specific circumstances. Here are a few demonstrations of the "ramming" method.

$\begingroup$Interesting, but "ramming" is better suited to clearing bowling pins off the alley than taking out printed objects of unknown bond strength to the substrate -- and unknown internal stress resistance :-($\endgroup$
– Carl WitthoftOct 19 '16 at 15:21

$\begingroup$I agree, Carl. Ramming would not be a good general solution and I expect would be poorly suited for anyone (like me) who prints a wide variety of objects and filaments. That said, it could be an adequate specific solution for a sufficiently narrow set of requirements. For example, ramming may be perfectly adequate for someone running a hypothetical "stretchlet factory." In contrast, I believe the first 3 methods are more viable for a broader range of prints, with the "eject and replace bed" method being potentially suitable for any print.$\endgroup$
– Chris ThompsonOct 19 '16 at 15:40

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$\begingroup$Edited the answer to remove the unintended suggestion that the ramming method was better than the other methods. :-)$\endgroup$
– Chris ThompsonOct 19 '16 at 15:51

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$\begingroup$ChrisThompson could you also add the suggestion by @fred_dot_u about the plowing method? That would make your answer a perfect reference for all future users :)$\endgroup$
– allanlaalOct 19 '16 at 20:19

From the standpoint of a hobbyist user with a mid-range machine, my answer is based on the model release from the build plate. With a heated clean glass plate, my model will almost always release once the plate has cooled. The "almost" aspect means that if you want to use the print head to push the model clear, you will be confronted with a stuck model occasionally.

The amount of force applied by the head may be enough to release a stuck model, but "may be" is not going to be sufficient. Especially with a core-xy system (used by my Emblaser laser engraver), you can either toss a belt or cause a stepper motor skipping. More powerful motors will reduce the skipping possibility, but not the belt jump problem.

You could consider to add one additional motor with a sweep arm, geared in such a manner as to provide the necessary torque, along with a force sensor to register a model stuck so badly as to be impossible to dislodge.

Your g-code would be written to lower the bed to the appropriate location to allow the sweep arm to operate, while the force sensor would be tied into the pause/stop circuit of your controller.

Some controllers already have the ability to manage an additional motor, as some are manufactured to provide for dual extrusion.

If such unattended operation is going to be a requirement, you'd also want some form of aborting a failing or failed print.

Here's a wild idea. Since you're planning to have a bed which only moves in the Z-axis, build a roller system which feeds a thin, flexible layer of some material (unobtanium, I fear) to cover the build plate. The feed rollers have a weak spring to provide some tension to keep this layer flat but not overly stretched while building the part. When the part is done, lower the bed to zero while allowing the roller to retract excess parts of the sheet (rollers on both sides of the build plate will have to do this). At zero, lock down the rollers and move the bed to some negative Z position, causing the overlay sheet to pop free of the bed and ideally pop the printed parts loose as well.